Question

Tanika asks Toby to multiply the expression 8^7* 8^3*8^2. Toby says he doesn't know how to do it, because he believes the Product of Powers works with only two exponential terms, and this problem has three terms. Explain how Toby could use the Product of Powers Property with three exponential terms.

Answer 1

Answer: 8^12

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Step-by-step explanation:

When working on complicated problems, it's best to break things down as much as possible.

Toby knows how to work with 2 terms, so let's start with that.

Ignore the 8^2 for now.

Focus on the first 2 exponential terms 8^7 and 8^3.

Multiply them to get: 8^7*8^3 = 8^(7+3) = 8^10

Which Toby should know how to do. The general rule is

a^b*a^c = a^(b+c)

Add the exponents but only when the bases are the same.

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This means

8^7* 8^3*8^2

is the same as

8^10*8^2

Then apply that rule again to get

8^10*8^2 = 8^(10+2) = 8^12

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So overall, 8^7*8^3*8^2 = 8^12

In other words, we add the exponents to get 7+3+2 = 12 as the final exponent. The base stays at 8 the entire time.