Find the numerical equivalent of 4^9⋅4^−7
Responses
4^2
4
4^16
16
The numerical equivalent of 4^9⋅4^−7 is 4^2, which is equal to 16.
can you explain
Certainly! To find the numerical equivalent of 4^9⋅4^−7, we can use the properties of exponents.
First, let's work with each exponent separately.
4^9 means to multiply 4 by itself 9 times: 4^9 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 262,144.
4^−7 means to take the reciprocal of 4^7. The reciprocal of 4^7 is 1 divided by 4^7: 4^−7 = 1/(4 * 4 * 4 * 4 * 4 * 4 * 4) = 1/16,384.
Now, let's multiply these values together:
4^9⋅4^−7 = 262,144 * (1/16,384) = 16.
So, the numerical equivalent of 4^9⋅4^−7 is 16.
To find the numerical equivalent of 4^9⋅4^−7, you can simplify the expression by combining the exponents. According to the laws of exponents, when you multiply two numbers with the same base, you add their exponents.
Hence, 4^9⋅4^−7 can be rewritten as 4^(9 + (-7)).
Simplifying further, 9 + (-7) equals 2. Thus, the numerical equivalent of 4^9⋅4^−7 is 4^2.
Therefore, the correct response is: 4^2.
To find the numerical equivalent of 4^9⋅4^−7, we can simplify the expression using the properties of exponents.
The property we need to use is the product of powers property, which states that when you multiply two powers with the same base, you add their exponents. Therefore, we can rewrite the expression as:
4^9⋅4^−7 = 4^(9 + -7)
Simplifying further, we have:
4^9⋅4^−7 = 4^2
Therefore, the numerical equivalent of 4^9⋅4^−7 is 4^2.
So the answer is: 4^2