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Sagot :
Let's find the values for each of the given mathematical expressions step-by-step.
### [tex]\( a) 6^2 - 6 \cdot 6 - 36 \)[/tex]
1. Calculate [tex]\( 6^2 \)[/tex]:
[tex]\[ 6^2 = 36 \][/tex]
2. Calculate [tex]\( 6 \cdot 6 \)[/tex]:
[tex]\[ 6 \times 6 = 36 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ 36 - 36 - 36 \][/tex]
4. Simplify the expression:
[tex]\[ 36 - 36 = 0 \][/tex]
[tex]\[ 0 - 36 = -36 \][/tex]
So, the value is [tex]\( -36 \)[/tex].
### [tex]\( b) (-6)^2 - 6 - 6 - 36 \)[/tex]
1. Calculate [tex]\( (-6)^2 \)[/tex]:
[tex]\[ (-6) \times (-6) = 36 \][/tex]
2. Substitute this value back into the equation and simplify:
[tex]\[ 36 - 6 - 6 - 36 \][/tex]
3. Combine like terms:
[tex]\[ 36 - 36 = 0 \][/tex]
[tex]\[ 0 - 6 - 6 = -12 \][/tex]
So, the value is [tex]\( -12 \)[/tex].
### [tex]\( i) \left(\frac{-3}{2}\right)^4 \)[/tex]
1. Calculate [tex]\( \left( \frac{-3}{2} \right)^4 \)[/tex]:
[tex]\[ \left( \frac{-3}{2} \right) \times \left( \frac{-3}{2} \right) \times \left( \frac{-3}{2} \right) \times \left( \frac{-3}{2} \right) \][/tex]
2. Multiply sequentially:
[tex]\[ \left( \frac{9}{4} \right) \times \left( \frac{9}{4} \right) = \left( \frac{81}{16} \right) \][/tex]
So, the value is [tex]\( 5.0625 \)[/tex].
### [tex]\( c) -62 - 6 - 6 \)[/tex]
1. Combine like terms directly:
[tex]\[ -62 - 6 - 6 = -74 \][/tex]
So, the value is [tex]\( -74 \)[/tex].
### [tex]\( j) \left(\frac{3}{2}\right)^3 \)[/tex]
1. Calculate [tex]\( \left( \frac{3}{2} \right)^3 \)[/tex]:
[tex]\[ \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \][/tex]
2. Multiply sequentially:
[tex]\[ \left( \frac{9}{4} \right) \times \left( \frac{3}{2} \right) = \left( \frac{27}{8} \right) \][/tex]
Noting that:
[tex]\[ \frac{27}{8} = 3.375 \][/tex]
So, the value is [tex]\( 3.375 \)[/tex].
### [tex]\( d) (-2)^3 - 2 \cdot (-2) \cdot (-2) \)[/tex]
1. Calculate [tex]\( (-2)^3 \)[/tex]:
[tex]\[ (-2) \times (-2) \times (-2) = -8 \][/tex]
2. Calculate [tex]\( 2 \cdot (-2) \cdot (-2) \)[/tex]:
[tex]\[ 2 \times (-2) \times (-2) = 8 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ -8 - 8 = -16 \][/tex]
So, the value is [tex]\( -16 \)[/tex].
### [tex]\( k) 0^{28} \)[/tex]
1. Any non-negative number to the power of zero is zero:
[tex]\[ 0^{28} = 0 \][/tex]
So, the value is [tex]\( 0 \)[/tex].
### [tex]\( e) -23 \)[/tex]
1. This is simply [tex]\( -23 \)[/tex], it remains unchanged.
### [tex]\( i2) 1^{32} \)[/tex]
1. Any number to the power of zero is one:
[tex]\[ 1^{32} = 1 \][/tex]
So, the value is [tex]\( 1 \)[/tex].
### [tex]\( m) (-1)^{20} \)[/tex]
1. Even powers of [tex]\( (-1) \)[/tex] result in [tex]\( 1 \)[/tex]:
[tex]\[ (-1)^{20} = 1 \][/tex]
So, the value is [tex]\( 1 \)[/tex].
### [tex]\( n) (-1)^{17} \)[/tex]
1. Odd powers of [tex]\( (-1) \)[/tex] result in [tex]\( -1 \)[/tex]:
[tex]\[ (-1)^{17} = -1 \][/tex]
So, the value is [tex]\( -1 \)[/tex].
### [tex]\( h) \left( \frac{3}{2} \right)^4 \)[/tex]
1. Calculate [tex]\( \left( \frac{3}{2} \right)^4 \)[/tex]:
[tex]\[ \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \][/tex]
2. Multiply sequentially:
[tex]\[ \left( \frac{9}{4} \right) \times \left( \frac{9}{4} \right) = \left( \frac{81}{16} \right) \][/tex]
Noting that:
[tex]\[ \frac{81}{16} = 5.0625 \][/tex]
So, the value is [tex]\( 5.0625 \)[/tex].
### [tex]\( o) \left( -\frac{3}{5} \right)^2 \)[/tex]
1. Calculate [tex]\( \left( -\frac{3}{5} \right)^2 \)[/tex]:
[tex]\[ \left( -\frac{3}{5} \right) \times \left( -\frac{3}{5} \right) = \left( \frac{9}{25} \right) \][/tex]
Noting that:
[tex]\[ \frac{9}{25} = 0.36 \][/tex]
So, the value is [tex]\( 0.36 \)[/tex].
### Summary
- [tex]\( a = -36 \)[/tex]
- [tex]\( b = -12 \)[/tex]
- [tex]\( i = 5.0625 \)[/tex]
- [tex]\( c = -74 \)[/tex]
- [tex]\( j = 3.375 \)[/tex]
- [tex]\( d = -16 \)[/tex]
- [tex]\( k = 0 \)[/tex]
- [tex]\( e = -23 \)[/tex]
- [tex]\( i2 = 1 \)[/tex]
- [tex]\( h = 5.0625 \)[/tex]
- [tex]\( m = 1 \)[/tex]
- [tex]\( n = -1 \)[/tex]
- [tex]\( o = 0.36 \)[/tex]
### [tex]\( a) 6^2 - 6 \cdot 6 - 36 \)[/tex]
1. Calculate [tex]\( 6^2 \)[/tex]:
[tex]\[ 6^2 = 36 \][/tex]
2. Calculate [tex]\( 6 \cdot 6 \)[/tex]:
[tex]\[ 6 \times 6 = 36 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ 36 - 36 - 36 \][/tex]
4. Simplify the expression:
[tex]\[ 36 - 36 = 0 \][/tex]
[tex]\[ 0 - 36 = -36 \][/tex]
So, the value is [tex]\( -36 \)[/tex].
### [tex]\( b) (-6)^2 - 6 - 6 - 36 \)[/tex]
1. Calculate [tex]\( (-6)^2 \)[/tex]:
[tex]\[ (-6) \times (-6) = 36 \][/tex]
2. Substitute this value back into the equation and simplify:
[tex]\[ 36 - 6 - 6 - 36 \][/tex]
3. Combine like terms:
[tex]\[ 36 - 36 = 0 \][/tex]
[tex]\[ 0 - 6 - 6 = -12 \][/tex]
So, the value is [tex]\( -12 \)[/tex].
### [tex]\( i) \left(\frac{-3}{2}\right)^4 \)[/tex]
1. Calculate [tex]\( \left( \frac{-3}{2} \right)^4 \)[/tex]:
[tex]\[ \left( \frac{-3}{2} \right) \times \left( \frac{-3}{2} \right) \times \left( \frac{-3}{2} \right) \times \left( \frac{-3}{2} \right) \][/tex]
2. Multiply sequentially:
[tex]\[ \left( \frac{9}{4} \right) \times \left( \frac{9}{4} \right) = \left( \frac{81}{16} \right) \][/tex]
So, the value is [tex]\( 5.0625 \)[/tex].
### [tex]\( c) -62 - 6 - 6 \)[/tex]
1. Combine like terms directly:
[tex]\[ -62 - 6 - 6 = -74 \][/tex]
So, the value is [tex]\( -74 \)[/tex].
### [tex]\( j) \left(\frac{3}{2}\right)^3 \)[/tex]
1. Calculate [tex]\( \left( \frac{3}{2} \right)^3 \)[/tex]:
[tex]\[ \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \][/tex]
2. Multiply sequentially:
[tex]\[ \left( \frac{9}{4} \right) \times \left( \frac{3}{2} \right) = \left( \frac{27}{8} \right) \][/tex]
Noting that:
[tex]\[ \frac{27}{8} = 3.375 \][/tex]
So, the value is [tex]\( 3.375 \)[/tex].
### [tex]\( d) (-2)^3 - 2 \cdot (-2) \cdot (-2) \)[/tex]
1. Calculate [tex]\( (-2)^3 \)[/tex]:
[tex]\[ (-2) \times (-2) \times (-2) = -8 \][/tex]
2. Calculate [tex]\( 2 \cdot (-2) \cdot (-2) \)[/tex]:
[tex]\[ 2 \times (-2) \times (-2) = 8 \][/tex]
3. Substitute these values back into the equation:
[tex]\[ -8 - 8 = -16 \][/tex]
So, the value is [tex]\( -16 \)[/tex].
### [tex]\( k) 0^{28} \)[/tex]
1. Any non-negative number to the power of zero is zero:
[tex]\[ 0^{28} = 0 \][/tex]
So, the value is [tex]\( 0 \)[/tex].
### [tex]\( e) -23 \)[/tex]
1. This is simply [tex]\( -23 \)[/tex], it remains unchanged.
### [tex]\( i2) 1^{32} \)[/tex]
1. Any number to the power of zero is one:
[tex]\[ 1^{32} = 1 \][/tex]
So, the value is [tex]\( 1 \)[/tex].
### [tex]\( m) (-1)^{20} \)[/tex]
1. Even powers of [tex]\( (-1) \)[/tex] result in [tex]\( 1 \)[/tex]:
[tex]\[ (-1)^{20} = 1 \][/tex]
So, the value is [tex]\( 1 \)[/tex].
### [tex]\( n) (-1)^{17} \)[/tex]
1. Odd powers of [tex]\( (-1) \)[/tex] result in [tex]\( -1 \)[/tex]:
[tex]\[ (-1)^{17} = -1 \][/tex]
So, the value is [tex]\( -1 \)[/tex].
### [tex]\( h) \left( \frac{3}{2} \right)^4 \)[/tex]
1. Calculate [tex]\( \left( \frac{3}{2} \right)^4 \)[/tex]:
[tex]\[ \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \times \left( \frac{3}{2} \right) \][/tex]
2. Multiply sequentially:
[tex]\[ \left( \frac{9}{4} \right) \times \left( \frac{9}{4} \right) = \left( \frac{81}{16} \right) \][/tex]
Noting that:
[tex]\[ \frac{81}{16} = 5.0625 \][/tex]
So, the value is [tex]\( 5.0625 \)[/tex].
### [tex]\( o) \left( -\frac{3}{5} \right)^2 \)[/tex]
1. Calculate [tex]\( \left( -\frac{3}{5} \right)^2 \)[/tex]:
[tex]\[ \left( -\frac{3}{5} \right) \times \left( -\frac{3}{5} \right) = \left( \frac{9}{25} \right) \][/tex]
Noting that:
[tex]\[ \frac{9}{25} = 0.36 \][/tex]
So, the value is [tex]\( 0.36 \)[/tex].
### Summary
- [tex]\( a = -36 \)[/tex]
- [tex]\( b = -12 \)[/tex]
- [tex]\( i = 5.0625 \)[/tex]
- [tex]\( c = -74 \)[/tex]
- [tex]\( j = 3.375 \)[/tex]
- [tex]\( d = -16 \)[/tex]
- [tex]\( k = 0 \)[/tex]
- [tex]\( e = -23 \)[/tex]
- [tex]\( i2 = 1 \)[/tex]
- [tex]\( h = 5.0625 \)[/tex]
- [tex]\( m = 1 \)[/tex]
- [tex]\( n = -1 \)[/tex]
- [tex]\( o = 0.36 \)[/tex]
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