Which exponent rule(s) would be used to simplify this expression? 2 x ^5⋅12x^−4 (1 point) Responses
The product exponent rule to add 5 + -4 to get an exponent of 1 on the x. You would also multiply 2 x 12 since they are coefficients.
The quotient rule to subtract 2 - 12 = -10. You would also subtract the exponents to get 5 - 4 = 1 for the power of x.
The power to power rule since you have two different exponents on the x, so the new exponent would be -20. Also, you would add 2 and 12 using the product rule for exponents.
The negative exponent rule to get 5 - (-4) = 9 for the power of x and then multiply 2 x 12 = 24 for the coefficient.
The product exponent rule to add 5 + -4 to get an exponent of 1 on the x. You would also multiply 2 x 12 since they are coefficients.
is this correct
Yes, that is correct. The product exponent rule states that when multiplying two powers with the same base, you add the exponents. In this case, adding the exponents 5 and -4 gives an exponent of 1 on the x. You would also multiply the coefficients 2 and 12.
Simplify 2 ⋅ 3^−4 / 5^−2
To simplify the expression 2 ⋅ 3^−4 / 5^−2, we can use the quotient and power of a power rules.
First, let's simplify the powers. According to the power of a power rule, when we have a power raised to another power, we multiply the exponents. So, 3^(-4) can be written as 1 / 3^4.
Next, we can substitute 1 / 3^4 into the expression:
2 ⋅ (1 / 3^4) / 5^(-2)
Now, according to the quotient rule, dividing by a negative exponent is the same as multiplying by the same base raised to the positive exponent. So, 5^(-2) can be written as 1 / 5^2.
Substituting 1 / 5^2 into the expression:
2 ⋅ (1 / 3^4) / (1 / 5^2)
Next, let's simplify the division by multiplying the numerator by the reciprocal of the denominator:
2 ⋅ (1 / 3^4) ⋅ (5^2 / 1)
Simplifying the numerators and denominators separately:
2 ⋅ (1 / 81) ⋅ 25
Now, we can simplify the expression further by multiplying the coefficients and the powers:
(2 ⋅ 25) / 81
Final Answer: 50 / 81