The expression [tex]5^{3} \times \sqrt{5}[/tex] written as a single power of 5 is [tex]5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
To write the given expression 5^3 x √5, as a single power of 5,
First, we will write the expression properly.
[tex]5^{3} \times \sqrt{5}[/tex]
Now, to write the above expression as a single power of 5,
First, express [tex]\sqrt{5}[/tex] in index form
By law of indices [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]
∴ [tex]\sqrt{5} = 5^{\frac{1}{2} }[/tex]
Now, the expression becomes
[tex]5^{3} \times 5^{\frac{1}{2} }[/tex]
Also, by law of indices, [tex]x^{y} \times x^{z} = x^{y+z}[/tex]
∴ [tex]5^{3} \times 5^{\frac{1}{2} } = 5^{3+\frac{1}{2} }[/tex]
[tex]= 5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
Hence, the expression [tex]5^{3} \times \sqrt{5}[/tex] written as a single power of 5 is [tex]5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
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