Is 7 to the 8th power times 7 equivalent to 7 to the the third power times 7 to third power equivalent?

They are not equivalent.

Step-by-step explanation:

Before we solve the question, we need to know that from the laws of indices:

A^x x A^y = A^(x+y).

7 to the power of 8th power means 7^8

7^8 times 7 means 7^8 x 7. From the laws of indices we have 7^8 x 7 = 7^9.

7 to the power of 3rd power means 7^3

7^3 times 7 to the power of 3rd power means 7^3 x 7^3. From the laws of indices we have 7^3 x 7^3 = 7^6.

Obviously, 7^9 ≠ 7^3 therefore, they are not equivalent.

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step-by-step explanation: