Use the product rule of exponents to simplify
3⁵ • 3⁷
A. 9³⁵
B. 3³⁵
C. 9¹²
D. 3¹²
To simplify the expression 3⁵ • 3⁷ using the product rule of exponents, you add the exponents together.
So, 3⁵ • 3⁷ = 3^(5+7) = 3¹².
Therefore, the answer is D. 3¹².
Find the numerical equivalent of
5¹⁰ • 5^-⁶
The answer should not contain any exponent expression or decimals.
To find the numerical equivalent of 5¹⁰ • 5^-⁶, we can use the quotient rule of exponents.
According to the quotient rule, when dividing two powers with the same base, you subtract the exponents.
So, 5¹⁰ • 5^-⁶ = 5^(10 - (-6)) = 5^(10 + 6) = 5^16.
Therefore, the numerical equivalent of 5¹⁰ • 5^-⁶ is 5^16.
To simplify the expression using the product rule of exponents, you multiply the bases (in this case 3) and add the exponents.
So 3⁵ • 3⁷ equals 3^(5+7), which simplifies to 3¹².
Therefore, the answer is D. 3¹².
To simplify the expression 3⁵ • 3⁷ using the product rule of exponents, you can add the exponents of the same base, which in this case is 3.
The product rule states that when you multiply two powers with the same base, you add their exponents.
So, applying the product rule, we can simplify the expression as follows:
3⁵ • 3⁷ = 3^(5 + 7) = 3¹²
Therefore, the simplified form of the expression 3⁵ • 3⁷ is 3¹².
The correct answer is D. 3¹².