To simplify the expression 15^0 ⋅ 7^−2 (−4)^−3, we can start by evaluating each term individually.
First, 15^0 is equal to 1. Any number raised to the power of 0 is always equal to 1.
Next, 7^−2 can be written as 1/7^2. A negative exponent indicates that the base should be moved to the denominator and the sign of the exponent should change. So 7^−2 is equivalent to 1/7^2.
Then, (−4)^−3 can be written as 1/(-4)^3. Here, the negative exponent similarly indicates that the base should be moved to the denominator and the sign of the exponent should change. So (−4)^−3 is equivalent to 1/(-4)^3.
Now, let's combine these individual expressions: 1 ⋅ 1/7^2 ⋅ 1/(-4)^3.
To simplify further, we can rewrite 1/7^2 as 7^−2.
So the expression becomes 1 ⋅ 7^−2 ⋅ 1/(-4)^3.
Next, we can rearrange the expression by placing the negative exponent before the base. So it becomes 1 ⋅ 7^−2 ⋅ (-4)^3.
Finally, applying the property of multiplying exponents with the same base, we can rewrite 7^−2 ⋅ (-4)^3 as (-4)^3/7^2.
Therefore, the equivalent expression to 15^0 ⋅ 7^−2 (−4)^−3 with only positive exponents is (-4)^3/7^2.
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?
explain how the answer is (−4)^3/7^2
1 answer