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Evaluate (7^5)^2*7^6

${(7^{5})}^{2} \cdot 7^{6}$

Step 1

Multiply the exponents in ${(7^{5})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$7^{5 \cdot 2} \cdot 7^{6}$

Multiply $5$ by $2$ .

$7^{10} \cdot 7^{6}$

$7^{10} \cdot 7^{6}$

Step 2

Multiply $7^{10}$ by $7^{6}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7^{10 + 6}$

Add $10$ and $6$ .

$7^{16}$

$7^{16}$

Step 3

Raise $7$ to the power of $16$ .

$33232930569601$

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