What is an expression equivalent to 7^-2•4^-2
An expression equivalent to 7^-2•4^-2 is (1/7^2) • (1/4^2)
To simplify the expression 7^-2 • 4^-2, we can first rewrite the negative exponents as their reciprocal powers. Negative exponents indicate that the base should be moved to the denominator of a fraction.
So, 7^-2 can be expressed as 1/7^2, and 4^-2 can be expressed as 1/4^2.
Now, substituting these values back into the original expression, we have (1/7^2) • (1/4^2).
Next, we can simplify the exponents by squaring both 7 and 4.
7^2 = 49
4^2 = 16
Substituting these values, the expression simplifies to (1/49) • (1/16).
Now, multiplying the fractions, we multiply the numerators and denominators together.
(1/49) • (1/16) = 1/(49 • 16).
Finally, we can compute the multiplication of 49 and 16 to get our simplified expression.
49 • 16 = 784.
So, the expression 7^-2 • 4^-2 is equivalent to the fraction 1/784.
To simplify the expression 7^-2 • 4^-2, we can rewrite the exponents as reciprocal powers of the base.
Recall that for any number x raised to the power of -n, it is equal to 1/x^n.
So, we can rewrite 7^-2 as 1/7^2 and 4^-2 as 1/4^2.
Now, we can rewrite the expression as follows:
1/7^2 • 1/4^2
Simplifying further, we can calculate the denominator by multiplying the bases:
1/49 • 1/16
To multiply these fractions, we multiply the numerators, then multiply the denominators:
1 * 1 / 49 * 16
The numerator is simply 1, and multiplying the denominators gives us:
1 / 784
Therefore, the expression 7^-2 • 4^-2 is equivalent to 1/784.