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1. Simplify the following expressions:

[tex]\[
\begin{array}{l}
a) \ (0.5) \times (0.5) \times (0.5) \times (0.5) \\
b) \ (-6) \times (-6) \times (-6) \\
c) \ 7 \times 7 \times 7 \times 7 \times 9 \times a \\
d) \ -(5 \times 5 \times 5)
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's work through the problem step-by-step.

### Step 1: Calculate [tex]\( a \)[/tex]
We need to multiply 0.5 by itself four times.

[tex]\[ a = 0.5 \times 0.5 \times 0.5 \times 0.5 = 0.0625 \][/tex]

### Step 2: Calculate [tex]\( B \)[/tex]
We need to multiply -6 by itself three times.

[tex]\[ B = (-6) \times (-6) \times (-6) = -216 \][/tex]

Note: Multiplying three negative factors yields a negative result.

### Step 3: Calculate [tex]\( c \)[/tex]
We need to multiply 7 by itself four times, multiply the result by 9, and then multiply the final result by [tex]\( a \)[/tex].

[tex]\[ c = 7 \times 7 \times 7 \times 7 \times 9 \times a = 1350.5625 \][/tex]

### Step 4: Calculate [tex]\( d \)[/tex]
We need to calculate the negative of 5 raised to the power of three.

[tex]\[ d = -1 \times (5 \times 5 \times 5) = -125 \][/tex]

Putting it all together, we have:
[tex]\[ a = 0.0625, \quad B = -216, \quad c = 1350.5625, \quad d = -125 \][/tex]

This gives us the final results:
[tex]\[ (a, B, c, d) = (0.0625, -216, 1350.5625, -125) \][/tex]
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