Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 /(−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

Question

Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 /(−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

Responses

4^3/7^2
Start Fraction 4 cubed over 7 squared end fraction

(−4)372
start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction

72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction

172 ⋅ (−4)−3

Answer 1

The correct expression is:

Start Fraction 4 cubed over 7 squared end fraction or 4^3/7^2.

Answer 2

To simplify the expression 15^0 ⋅ 7^−2 /(−4)^−3 with only positive exponents using the properties of integer exponents, we can first apply the rule that any number raised to the power of 0 is equal to 1.

So, 15^0 becomes 1.

Next, we can use the rule that when we have a negative exponent, we can rewrite it as the reciprocal of the positive exponent.

Therefore, 7^−2 becomes 1/7^2.

Similarly, (−4)^−3 becomes 1/(−4)^3.

Now, we can simplify the expression:

1 ⋅ 1/7^2 / 1/(−4)^3

Simplifying further:

1/1 ⋅ 1/7^2 / 1/(-4)^3

Since 1/1 is equal to 1, we can ignore it:

1/7^2 / 1/(-4)^3

Finally, we can simplify the expression by multiplying the fractions:

1*(−4)^3/7^2

So, the equivalent expression with only positive exponents is:

(−4)^3/7^2

Answer 3

To find the equivalent expression with only positive exponents, we can apply the properties of integer exponents. Here's how you can simplify the given expression:

First, let's address the negative exponents:

15^0 = 1 (any non-zero number raised to the power of 0 is 1)
7^(-2) = 1/7^2 (a negative exponent can be rewritten as the reciprocal of the positive exponent)
(-4)^(-3) = 1/(-4)^3 (same rule applies here)

Now, let's simplify the expression:

1 * (1/7^2) * (1/(-4)^3)

To simplify further, let's work out the values:

1 * (1/49) * (1/(-64))

Now, let's combine the fractions:

1/49 * 1/(-64) = 1/(-3136)

Finally, let's rewrite the negative exponent as a positive one:

1/(-3136) = -1/3136

Therefore, the expression equivalent to 15^0 ⋅ 7^(-2) / (-4)^(-3) with only positive exponents is -1/3136. So, none of the given responses matches the equivalent expression.