Answer:
[tex]\frac{7^{18}}{7^{9}}[/tex], (7³)³ and [tex]7^{4}*7^{5}[/tex]
Step-by-step explanation:
[tex]7^{8}*7[/tex] = [tex]7^{9}[/tex] is equivalent to the following exponential expressions:
[tex]\frac{7^{18}}{7^{9}}[/tex], as it applies to the Quotient Rule of Exponents: [tex]\frac{a^{m}}{a^{n}} = a^{m-n}[/tex]. Therefore, you're essentially subtracting the exponents, resulting into [tex]7^{9}[/tex].
(7³)³: The Power-to-Power Rule of Exponents apply in this situation:[tex](a^{m})^{n} = a^{mn}[/tex]. Multiplying the exponent inside the parenthesis by the exponent outside the parenthesis results in an exponent of 9.
[tex]7^{4}*7^{5}[/tex]: the Product Rule of Exponents apply in this situation: [tex]a^{m}*a^{n} = a^{m+n}[/tex]. Adding the exponents of 4 to 5 results in an exponent of 9.
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