Which expression is equivalent to 3, to the power minus 4 , times, 3, to the power 6 , question mark3
−4
×3
6
?
The expression that is equivalent to 3 to the power of -4 times 3 to the power of 6 is 3 to the power of (6-4).
This simplifies to 3 to the power of 2, which is equal to 9.
So, the expression is equal to 9.
To find the equivalent expression, we can simplify each part of the expression and then multiply them together.
First, let's simplify 3 to the power -4. Any number raised to the power of -n is equal to 1 divided by that number raised to the power of n. Therefore, 3 to the power -4 is equal to 1 divided by 3 to the power 4.
1 / (3^4) = 1 / (3 * 3 * 3 * 3) = 1 / 81
Next, let's simplify 3 to the power 6. 3 to the power 6 is calculated by multiplying 3 by itself six times.
3^6 = 3 * 3 * 3 * 3 * 3 * 3 = 729
Finally, let's multiply these two simplified expressions together.
(1 / 81) * 729
To multiply fractions, we multiply the numerators and multiply the denominators.
1 * 729 = 729
81 * 1 = 81
So, the equivalent expression is 729/81.
To find an expression equivalent to 3 to the power of minus 4 times 3 to the power of 6, we can use the rule of exponents that states when raising a number with an exponent to another exponent, we multiply the exponents.
In this case, we have:
3^(-4) * 3^6
To combine the exponents, we can add them together:
3^(-4 + 6)
Simplifying further:
3^2
So, the expression equivalent to 3 to the power of minus 4 times 3 to the power of 6 is 3 raised to the power of 2.