Question

Write the expression as an exponent:

5^8 x 25
6^15 x 36

Answer 1

`\displaystyle {5}^(10)`

`\displaystyle {6}^(17)`

Explanation:

Question-1:

we want to rewrite the following expression as an exponent

`\displaystyle {5}^(8) * {25}`

remember that 25 is the square of 5 therefore

`\displaystyle {5}^(8) * {5}^(2)`

recall that,

`\displaystyle {x}^(m) * {x}^(n) = {x}^(m + n)`

with that law we obtain:

`\displaystyle {5}^(8 + 2)`

simplify addition:

`\displaystyle {5}^(10)`

Question-2:

likewise Question-1 36 is the square of 6 Thus,

`\displaystyle {6}^(15) * {6}^(2)`

similarly apply law of exponent:

`\displaystyle {6}^(15 + 2)`

simplify addition:

`\displaystyle {6}^(17)`

hence,

we have written the expression as an exponent

Answer 2

a.) 5¹⁰

b.) 6¹⁷

Explanation:

a.) 5⁸ × 25

Write 25 in the exponential form with the base of 5.

• 5⁸ × 5²

To calculate product use exponent rule

• 5⁸+²
• 5¹⁰

b.) 6¹⁵ × 36

Similarly, 6¹⁵ × 36

Write 25 in the exponential form with the base of 6.

• 6¹⁵ × 6²

To calculate product use exponent rule.

• 6¹⁵ + ²
• 6¹⁷