Find the numerical equivalent of 4^9⋅4^−7
Responses
4^2
4
4^16
16
3 answers
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.
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.