Apply the Property of Negative Integer Exponents to rewrite 15^−38 as an expression with positive exponents only.
The property of negative integer exponents states that a number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent.
So, applying this property to rewrite 15^−38, we have:
15^−38 = 1 / 15^38
The property of negative integer exponents states that a number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent.
So, applying this property to rewrite 9^−23, we have:
9^−23 = 1 / 9^23
The property of negative integer exponents states that a number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent.
So, applying this property and simplifying, we have:
3^−4 = 1 / 3^4
Now, let's simplify 3^4:
3^4 = 3 × 3 × 3 × 3 = 81
Therefore:
3^−4 = 1 / 81
To generate an expression equivalent to 7^−3 ⋅ 7^−5 with positive exponents only, we can apply the property of negative integer exponents which states that when multiplying the same base raised to negative exponents, the exponents can be combined by adding them and then taking the reciprocal.
So, let's apply the property:
7^−3 ⋅ 7^−5 = 1/7^3 ⋅ 1/7^5
Now, let's combine the exponents:
1/7^3 ⋅ 1/7^5 = 1/7^(3+5)
Simplifying further, we get:
1/7^(3+5) = 1/7^8
Therefore, an expression equivalent to 7^−3 ⋅ 7^−5 with positive exponents only is 1/7^8.
To generate an expression equivalent to 5^(-9)/4^(-12) with positive exponents only, we can apply the property of negative integer exponents that states when a number with a negative exponent is in the denominator, the negative exponent can be moved to the numerator and become positive.
So, in this case, we have:
5^(-9)/4^(-12)
Applying the property, we can move the negative exponents to the numerator:
= 4^(12)/5^(9)
Therefore, an expression equivalent to 5^(-9)/4^(-12) with positive exponents only is 4^(12)/5^(9).
The expression that is equivalent to 1/8^5 is 8^(-5).
So, the correct option is 8^−5.
To generate an equivalent expression to 13^−5 ⋅13^−11 with only positive exponents, we can apply the property that states when multiplying two bases with negative exponents, the exponents can be combined by adding them and then taking the reciprocal.
So, in this case, we have 13^−5 ⋅13^−11.
Applying the property, we can combine the exponents:
= 1/13^(5 + 11)
= 1/13^16
Therefore, an equivalent expression to 13^−5 ⋅13^−11 with only positive exponents is 1/13^16.
So, the correct option is 1/13^16.
To generate an equivalent expression to 7^3/25^−4 with only positive exponents, we can apply the property of negative integer exponents, which states that when a number with a negative exponent is in the denominator, the negative exponent can be moved to the numerator and become positive.
So, in this case, we have 7^3/25^−4.
Applying the property, we can move the negative exponent to the numerator:
= 7^3 * 25^4
Therefore, an equivalent expression to 7^3/25^−4 with only positive exponents is 7^3 * 25^4.
So, the correct option is 7^3⋅25^4.