Answer :
Answer:
[tex]\sqrt{63}\times \sqrt[3]{56}\times7^{\frac{1}{6}}=42[/tex]
Step-by-step explanation:
Given : Expression [tex]\sqrt{63}\times \sqrt[3]{56}\times7^{\frac{1}{6}}[/tex]
To find : What is the value of the expression ?
Solution :
Step 1 - Write the expression as
[tex](63)^{\frac{1}{2}}\times(56)^{\frac{1}{3}}\times7^{\frac{1}{6}}[/tex]
Step 2 - Factor 63 and 56 as multiple of 7,
[tex](7\times 9)^{\frac{1}{2}}\times(7\times 8)^{\frac{1}{3}}\times7^{\frac{1}{6}}[/tex]
Step 3 - Split the powers [tex](a\times b)^c=a^c\times b^c[/tex]
[tex]7^{\frac{1}{2}}\times 9^{\frac{1}{2}}\times7^{\frac{1}{3}}\times 8^{\frac{1}{3}}\times7^{\frac{1}{6}}[/tex]
Step 4 - Add the same base power, [tex]a^b\times a^c=a^{b+c}[/tex]
[tex]=7^{\frac{1}{2}+\frac{1}{3}+\frac{1}{6}}\times (3^2)^{\frac{1}{2}}\times (2^3)^{\frac{1}{3}}[/tex]
[tex]=7^{\frac{3+2+1}{6}}\times (3)^{\frac{2}{2}}\times (2)^{\frac{3}{3}}[/tex]
[tex]=7^{\frac{6}{6}}\times (3)^{1}\times (2)^{1}[/tex]
[tex]=7\times3\times2[/tex]
[tex]=42[/tex]
Therefore, [tex]\sqrt{63}\times \sqrt[3]{56}\times7^{\frac{1}{6}}=42[/tex]