An exponent, also known as a power, indicates repeated multiplication of the same quantity. For example, we can write 2∙2∙2∙2 in exponential notation as 2 to the power of 4, where 2 is the base and 4 is the exponent (or power). We can read this as 2 to the fourth power or 2 to the power of 4. This module will review the properties of exponents that can be used to simplify expressions containing exponents.
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Simplify the expression: open parenthesis p to the power of 9 q to the power of negative two close parenthesis open parenthesis p to the power of negative six q squared close parenthesis.
Line 1. Use the product property and add the exponents of the same bases: p to the power of 6 plus negative 9 end superscript q to the power of negative 2 plus 2 end superscript.
Line 2. Simplify the exponents: p cubed q to the power of 0.
Line 3. Use the zero exponent property: p cubed times 1.
Line 4. Simplify to the final expression: p cubed.
Simplify the expression: Fraction: open parenthesis y squared close parenthesis cubed open parenthesis y squared close parenthesis to the power of 4 over open parenthesis y to the power of 5 close parenthesis to the power of 4 end fraction.
Line 1. Use the power property. Begin Fraction: Open parenthesis y to the 2 times 3 end superscript close parenthesis open parenthesis y to the 2 times 4 end superscript close parenthesis over y to the 5 times 4 end superscript end fraction.
Line 2. Multiply the exponents to simplify. Begin fraction: y to the 6 y to the 8 over y to the 20, end fraction.
Line 3. Use the product property in the numerator. Begin fraction: y to the 6 plus 8 end superscript over y to the 20, end fraction.
Line 4. Add the exponents to simplify. Begin fraction: y to the 14 over y to the 20, end fraction
Line 5. Use the quotient property. y to the 14 minus 20 end superscript.
Line 6. Subtract the exponents to simplify. y to the negative 6.
Line 7. Write negative exponents as positive for final answer. Begin fraction: 1 over y to the 6, end fraction.Simplify the expression: Open parenthesis begin fraction 2x cubed over 3y end fraction close parenthesis to the power of 4.
Line 1. Raise the numerator and a denominator to the power of 4 using the quotient to a power property. Begin fraction: open parenthesis 2x cubed close parenthesis to the power of 4 over open parenthesis 3y close parenthesis to the power of 4, end fraction.
Line 2. Raise each factor to the power of 4 using the Product to a Power Property. Begin fraction: 2 to the power of 4 open parenthesis x cubed close parenthesis to the power of 4 over 3 to the power of 4 y to the power of 4, end fraction.
Line 3: Apply exponents and use the Power Property to simplify. Begin fraction: 16 x to the power of 12 over 81 y to the power of 4, end fraction.
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window