Exponents - Algebra II

Card 0 of 3072

Question

Simplify $x^5y^2x^{-4}$

Answer

First, combine exponents of like variables. This gives us

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Question

Simplify $z^3y^2x^6y^{-3}$

Answer

First, combine exponents of like variables. This gives us $z^3y^{-1}x^6$ which simplifies to $\frac{z^3x^6}{y}$

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Question

Expand:

Answer

To expand the exponent, we multiply the base by whatever the exponent is.

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Question

Evaluate: $\frac{3}{x^0+y^0}$

Answer

Although we have two variables, we do know that a number raised to a zero power is one. Therefore:

$\frac{3}{x^0+y^0}=\frac{3}{1+1}=\frac{3}{2}$

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Question

Simplify.

$3^{-14}3^{23}3^{-15}$

Answer

When multiplying exponents with the same base, you just have to add the exponents.

$3^{-14}3^{23}3^{-15}=3^{-14+23-15}=3^{-6}$

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Question

Simplify.

$\frac{a^{45}}{a^{30}}$

Answer

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{45}}{a^{30}}=a^{45-30}=a^{15}$

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Question

Simplify.

$\frac{a^7}{a^{18}}$

Answer

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{7}}{a^{18}}=a^{7-18}=a^{-11}$

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Question

Simplify: $12^{19}\div12^7$

Answer

When dividing exponents with the same base, we subtract the exponents and keep the base the same.

$12^{19}\div12^7=12^{19-7}=12^{12}$

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Question

Simplify:

Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$23^7*23^8=23^{7+8}=23^{15}$

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Question

Simplify: $2^4*2^{-12}$

Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$2^4*2^{-12}=2^{4+(-12)}=2^{-8}$

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Question

Simplify: $(-3)^7*(-3)^{-2}$

Answer

When multiplying exponents with the same base, we add the exponents and keep the base the same.

$(-3)^7*(-3)^{-2}=(-3)^{7+(-2)}=(-3)^{5}$

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Question

Simplify:

Answer

When multiplying exponents with the same base, we just keep the base the same and add the exponents.

$x^5*x^6=x^{5+6}=x^{11}$

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Question

Simplify: $x^{12}*x^{-8}$

Answer

When multiplying exponents with the same base, we just keep the base the same and add the exponents.

$x^{12}*x^{-8}=x^{12+(-8)}=x^4$

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Question

Simplify:

$(5^{-8})^{-12}$

Answer

When dealing with exponents being raised by another exponent, we just multiply the powers and keep the base the same.

$(5^{-8})^{-12}=5^{-8*-12}=5^{96}$

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Question

Simplify: $(3a^2b^{-3}c^4)^2$

Answer

To simplify this expression, square every term in the parentheses:

$3^2a^4b^{-6}c^8$ .

Then simplify and get rid of the negative exponent by putting the b term on the denominator:

$\frac{9a^4c^8}{b^6}$ .

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Question

Simplify:

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(4^7)^7=4^{7*7}=4^{49}$

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Question

What is $5^{-2}$ the same as?

Answer

While a positive exponent says how many times to multiply by a number, a negative exponent says how many times to divide by the number.

To solve for negative exponents, just calculate the reciprocal.

$5^{-2}=\frac{1}{5^{2}}=\frac{1}{25}$

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Question

Solve: $32^{-\frac{1}{5}}$

Answer

To evaluate a negative exponent, convert the exponent to positive by taking the inverse.

$32^{-\frac{1}{5}}= \frac{1}{32^{\frac{1}{5}}}=\frac{1}{2}$

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Question

Simplify:

$(8^7)^{-2}$

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(8^7)^{-2}=8^{7*-2}=8^{-14}$

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Question

Simplify:

$(5^{-5})^{-5}$

Answer

When an exponent is raised by another exponent, we will multiply the exponents and keep the base the same.

Simplify:

$(5^{-5})^{-5}=5^{-5*-5}=5^{25}$

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