10. Apply the Properties of Integer Exponents to generate equivalent expressions with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

Question

(4^3 * 7^-2)^-5
7^9 * 4^-13
*
1 point
7/16
21/28
-7/16
16

Answer 1

To apply the properties of integer exponents, we can use the rule that states for any nonzero number a, and integers m and n:

(a^m)^n = a^(m*n)

Using this rule, we can rewrite the expression (4^3 * 7^-2)^-5 as 4^(3*(-5)) * 7^(-2*(-5)). This becomes:

4^(-15) * 7^10

Now, to generate equivalent expressions with only positive exponents, we can use the rule that states for any nonzero number a:

a^-n = 1/a^n

Using this rule, we can rewrite 4^(-15) as 1/(4^15), and 7^10 as 1/(7^-10). This gives us:

1/(4^15) * 1/(7^-10)

Applying the rule that states for any nonzero numbers a and b:

1/a * 1/b = 1/(a*b)

We can simplify the expression further to:

1/(4^15 * 7^-10)

Now, to multiply the powers with the same base, we can use the rule that states for any nonzero number a, and integers m and n:

a^m * a^n = a^(m+n)

Using this rule, we can simplify the expression to:

1/(4^15 * 7^-10) = 1/(4^(15+10)*7^(-10))

So the final expression is:

1/(4^25 * 7^-10)

This can be written as a fraction with positive exponents by applying the rule that states for any nonzero number a:

a^-n = 1/a^n

Thus, 7^-10 becomes 1/7^10:

1/(4^25 * 1/7^10)

Multiplying the fractions:

1/(4^25 * 1/7^10) = 7^10/4^25

Simplifying further:

7^10/4^25 = (7/4)^10

So the equivalent expression with only positive exponents is (7/4)^10.

To solve this expression, we can raise 7/4 to the power of 10:

(7/4)^10 = 282475249/1048576

Thus, the simplified fraction with no remaining exponents is 282475249/1048576.

So the answer is: 282475249/1048576 (Option: D)

Answer 2

Just the naswer pllz

Answer 3

The answer is 1073741824/8303765625.

Answer 4

That is not one of the choices

7/16
21/28
-7/16
16

Answer 5

Apologies for the confusion. The correct answer is 7/16.