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Simplify. Write the expression using only positive exponents.$8^{-2}\cdot a^7$8−2·a7​The simplified expression is

Question

Simplify. Write the expression using only positive exponents.82a78^{-2}\cdot a^78−2·a7​The simplified expression is

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Solution

To simplify the expression 82a78^{-2}\cdot a^7, we need to apply the rule that any number to the power of -n is equal to 1 divided by that number to the power of n.

Step 1: Rewrite 828^{-2} as 182\frac{1}{8^2}.

Step 2: Calculate 828^2 which is 64.

Step 3: Substitute 828^2 with 64 in the expression, so we get 164a7\frac{1}{64}\cdot a^7.

So, the simplified expression is 164a7\frac{1}{64}a^7.

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