How to evaluate exponents

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Math › How to evaluate exponents

Questions 1 - 10

Which of the following is equivalent to ?

$X^{10}$

$X^{7}$

$X^{5}$

$X^{3}$

$X^{25}$

Explanation

When an exponent expression is raised by another exponent, you can multiply the exponents:

$(X^{2})^{5}=X^{2 \cdot 5}=X^{10}$

Which of the following is equivalent to ?

$X^{10}$

$X^{7}$

$X^{5}$

$X^{3}$

$X^{25}$

Explanation

When an exponent expression is raised by another exponent, you can multiply the exponents:

$(X^{2})^{5}=X^{2 \cdot 5}=X^{10}$

What is the value of 93?

Explanation

Exponents are a way of expressing the repeated multiplication of the same value. An exponent describes how many times a value is to be multiplied by itself.

$9^{3}=9\cdot 9\cdot 9=729$

What is the value of 93?

Explanation

Exponents are a way of expressing the repeated multiplication of the same value. An exponent describes how many times a value is to be multiplied by itself.

$9^{3}=9\cdot 9\cdot 9=729$

Evaluate $\dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}$

$x^{2x^{2}-5x+13}$

$x^{4x-7}$

$\dpi{100} x^{4x^{2}-10x+26}$

$\dpi{100} x^{x^{2}-x+7}$

$\dpi{100} x^{x^{2}-2x+6}$

Explanation

The quotient rule for exponents states that when like numbers are raised to a certain power, then their exponents are subtracted from one another.

$\dpi{100} \dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}=x^{(4x^{2}-3x+7)-(2x^{2}+2x-6)}$

Solve for the exponent equation.

$(4x^{2}-3x+7)-(2x^{2}+2x-6)=4x^{2}-3x+7-2x^{2}-2x+6$

Combine like terms.

$\rightarrow (2x^{2}-5x+13)$

Therefore,

$\dpi{100} \dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}=x^{2x^{2}-5x+13}$

Which of the following is a simplified expression of X3X2?

$X^{5}$

$X^{6}$

$X\cdot 6$

$X^{1}$

$X\cdot X^{2}$

Explanation

When you multiply two exponential expressions with the same base, add the exponents to simplify the expression.

$X^{3}X^{2}=X^{5}$

Which of the following is a simplified expression of X3X2?

$X^{5}$

$X^{6}$

$X\cdot 6$

$X^{1}$

$X\cdot X^{2}$

Explanation

When you multiply two exponential expressions with the same base, add the exponents to simplify the expression.

$X^{3}X^{2}=X^{5}$

Simplify the exponential expression.

$\small [(3x^2y^2)(4xy^3)]^0$

$\small 12x^3y^5$

undefined

Explanation

$\small [(3x^2y^2)(4xy^3)]^0$

Any number to the "zero" power is equal to .

$\small [(3x^2y^2)(4xy^3)]^0=[12x^3y^5]^0=1$

Evaluate $\dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}$

$x^{2x^{2}-5x+13}$

$x^{4x-7}$

$\dpi{100} x^{4x^{2}-10x+26}$

$\dpi{100} x^{x^{2}-x+7}$

$\dpi{100} x^{x^{2}-2x+6}$

Explanation

The quotient rule for exponents states that when like numbers are raised to a certain power, then their exponents are subtracted from one another.

$\dpi{100} \dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}=x^{(4x^{2}-3x+7)-(2x^{2}+2x-6)}$

Solve for the exponent equation.

$(4x^{2}-3x+7)-(2x^{2}+2x-6)=4x^{2}-3x+7-2x^{2}-2x+6$

Combine like terms.

$\rightarrow (2x^{2}-5x+13)$

Therefore,

$\dpi{100} \dpi{100} \frac{x^{(4x^{2}-3x+7)}}{x^{(2x^{2}+2x-6)}}=x^{2x^{2}-5x+13}$

Simplify the exponential expression.

$\small [(3x^2y^2)(4xy^3)]^0$

$\small 12x^3y^5$

undefined

Explanation

$\small [(3x^2y^2)(4xy^3)]^0$

Any number to the "zero" power is equal to .

$\small [(3x^2y^2)(4xy^3)]^0=[12x^3y^5]^0=1$

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