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Calculate the powers:

[tex]\[
\begin{array}{l}
a) 6^2 = 6 \cdot 6 = 36 \\
b) (-6)^2 = (-6) \cdot (-6) = 36 \\
c) -6^2 = -(6 \cdot 6) = -36 \\
d) (-2)^3 = -2 \cdot -2 \cdot -2 = -8 \\
e) -2^3 = -(2 \cdot 2 \cdot 2) = -8 \\
f) (-8)^0 = 1 \\
g) 1^{32} = 1 \\
h) \left(\frac{3}{2}\right)^4 = \left(\frac{3}{2}\right) \cdot \left(\frac{3}{2}\right) \cdot \left(\frac{3}{2}\right) \cdot \left(\frac{3}{2}\right) = \frac{81}{16} \\
i) \left(-\frac{3}{2}\right)^4 = \left(-\frac{3}{2}\right) \cdot \left(-\frac{3}{2}\right) \cdot \left(-\frac{3}{2}\right) \cdot \left(-\frac{3}{2}\right) = \frac{81}{16} \\
j) \left(\frac{3}{2}\right)^3 = \left(\frac{3}{2}\right) \cdot \left(\frac{3}{2}\right) \cdot \left(\frac{3}{2}\right) = \frac{27}{8} \\
k) 0^{28} = 0 \\
l) (-1)^{20} = 1 \\
m) (-1)^{17} = -1 \\
n) \left(-\frac{3}{5}\right)^2 = \left(-\frac{3}{5}\right) \cdot \left(-\frac{3}{5}\right) = \frac{9}{25} \\
\end{array}
\][/tex]

Note: Ensure each calculation is verified for accuracy.

Sagot :

GinnyAnsweridn
Sure! Let's go through the calculations step-by-step for each expression you have given.

a) [tex]\( 6^2 \)[/tex]
[tex]\[ 6 \times 6 = 36 \][/tex]

b) [tex]\( (-6)^2 \)[/tex]
[tex]\[ (-6) \times (-6) = 36 \][/tex]

c) [tex]\(-6^2\)[/tex]
[tex]\[ - (6 \times 6) = -36 \][/tex]

d) [tex]\( (-2)^3 \)[/tex]
[tex]\[ (-2) \times (-2) \times (-2) = -8 \][/tex]

i) [tex]\( \left(-\frac{3}{2}\right)^4 \)[/tex]
[tex]\[ \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right) \times \left(-\frac{3}{2}\right) = 5.0625 \][/tex]

J) [tex]\( \left(\frac{3}{2}\right)^1 \)[/tex]
[tex]\[ \left(\frac{3}{2}\right) = 1.5 \][/tex]

k) [tex]\( 0^{28} \)[/tex]
[tex]\[ 0^{28} = 0 \][/tex] (As long as the exponent is positive and the base is 0)

e) [tex]\( -2^3 \)[/tex]
[tex]\[ - (2 \times 2 \times 2) = -8 \][/tex]

[tex]\( 715^\circ \)[/tex]
This number is as is, [tex]\( 715 \)[/tex].

9) [tex]\( (-8)^0 \)[/tex]
[tex]\[ (-8)^0 = 1 \][/tex] (Any non-zero number raised to the power of 0 equals 1)

i) [tex]\( 1^{32} \)[/tex]
[tex]\[ 1^{32} = 1 \][/tex] (Any number raised to any power, if the base is 1, the result is always 1)

h) [tex]\( \left(\frac{3}{2}\right)^4 \)[/tex]
[tex]\[ \left(\frac{3}{2}\right) \times \left(\frac{3}{2}\right) \times \left(\frac{3}{2}\right) \times \left(\frac{3}{2}\right) = 5.0625 \][/tex]

m) [tex]\( (-1)^{20} \)[/tex]
[tex]\[ m = (-1)^{20} = 1 \][/tex] (Any even power of -1 equals 1)

n) [tex]\( (-1)^{17} \)[/tex]
[tex]\[ n = (-1)^{17} = -1 \][/tex] (Any odd power of -1 equals -1)

b) [tex]\( \left(-\frac{3}{5}\right)^2 \)[/tex]
[tex]\[ \left(-\frac{3}{5}\right) \times \left(-\frac{3}{5}\right) = \left(\frac{9}{25}\right) = 0.36 \][/tex]

And that's the step-by-step calculation for each given expression.
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