At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To solve the expression [tex]\( 8^{\frac{8}{3}} \)[/tex], follow these steps:
1. Identify the base and the exponent: Here, the base is [tex]\( 8 \)[/tex] and the exponent is [tex]\( \frac{8}{3} \)[/tex].
2. Express the exponent in fractional form: The exponent [tex]\( \frac{8}{3} \)[/tex] is already in fractional form. This can be interpreted as raising the base to a power and then taking the cube root.
3. Simplify the base if possible: In this case, the base [tex]\( 8 \)[/tex] can be expressed as [tex]\( 2^3 \)[/tex]. So,
[tex]\[ 8 = 2^3 \][/tex]
This transforms the equation to:
[tex]\[ 8^{\frac{8}{3}} = (2^3)^{\frac{8}{3}} \][/tex]
4. Apply the power of a power property: According to the properties of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
[tex]\[ (2^3)^{\frac{8}{3}} = 2^{3 \cdot \frac{8}{3}} \][/tex]
5. Simplify the exponent: Multiply the exponents:
[tex]\[ 3 \cdot \frac{8}{3} = 8 \][/tex]
So, we get:
[tex]\[ 2^8 \][/tex]
6. Calculate the final result: Raise [tex]\( 2 \)[/tex] to the power of 8:
[tex]\[ 2^8 = 256 \][/tex]
Therefore, the value of [tex]\( 8^{\frac{8}{3}} \)[/tex] is [tex]\( 256 \)[/tex]. Given in the context, due to rounding and precision, the final answer is:
[tex]\[ 8^{\frac{8}{3}} \approx 255.99999999999991 \][/tex]
1. Identify the base and the exponent: Here, the base is [tex]\( 8 \)[/tex] and the exponent is [tex]\( \frac{8}{3} \)[/tex].
2. Express the exponent in fractional form: The exponent [tex]\( \frac{8}{3} \)[/tex] is already in fractional form. This can be interpreted as raising the base to a power and then taking the cube root.
3. Simplify the base if possible: In this case, the base [tex]\( 8 \)[/tex] can be expressed as [tex]\( 2^3 \)[/tex]. So,
[tex]\[ 8 = 2^3 \][/tex]
This transforms the equation to:
[tex]\[ 8^{\frac{8}{3}} = (2^3)^{\frac{8}{3}} \][/tex]
4. Apply the power of a power property: According to the properties of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
[tex]\[ (2^3)^{\frac{8}{3}} = 2^{3 \cdot \frac{8}{3}} \][/tex]
5. Simplify the exponent: Multiply the exponents:
[tex]\[ 3 \cdot \frac{8}{3} = 8 \][/tex]
So, we get:
[tex]\[ 2^8 \][/tex]
6. Calculate the final result: Raise [tex]\( 2 \)[/tex] to the power of 8:
[tex]\[ 2^8 = 256 \][/tex]
Therefore, the value of [tex]\( 8^{\frac{8}{3}} \)[/tex] is [tex]\( 256 \)[/tex]. Given in the context, due to rounding and precision, the final answer is:
[tex]\[ 8^{\frac{8}{3}} \approx 255.99999999999991 \][/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.