<< Chapter < Page | Chapter >> Page > |
The following examples suggest a rule for raising a power to a power:
To raise a power to a power, multiply the exponents.
Simplify each expression using the power rule for powers. All exponents are natural numbers.
Although we don’t know exactly what number is, the notation indicates the multiplication.
Simplify each expression using the power rule for powers.
The following examples suggest a rule for raising a product to a power:
To raise a product to a power, apply the exponent to each and every factor.
Make use of either or both the power rule for products and power rule for powers to simplify each expression.
Make use of either or both the power rule for products and the power rule for powers to simplify each expression.
The following example suggests a rule for raising a quotient to a power.
To raise a quotient to a power, distribute the exponent to both the numerator and denominator.
Make use of the power rule for quotients, the power rule for products, the power rule for powers, or a combination of these rules to simplify each expression. All exponents are natural numbers.
Make use of the power rule for quotients, the power rule for products, the power rule for powers, or a combination of these rules to simplify each expression.
Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers.
( [link] ) Is there a smallest integer? If so, what is it?
no
( [link] ) Use the distributive property to expand .
( [link] ) Assuming the bases are not zero, find the value of .
( [link] ) Assuming the bases are not zero, find the value of .
Notification Switch
Would you like to follow the 'Elementary algebra' conversation and receive update notifications?