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Simplifying expressions from $2^m2^n$ to $2^{m+n}$.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following as a single power of 2.

\\[2^\\var{m}\\times 2^\\var{n}\\]

", "advice": "

To simplify $2^\\var{m}\\times 2^\\var{n}$, we want to make use of the following rule:

\\[a^n \\times a^m = a^{n+m}\\]

Applying this rule,

\\[\\begin{split}2^\\var{m}\\times 2^\\var{n} &\\,=2^{\\simplify[!collectNumbers]{{m}+{n}}}\\\\ \\\\&\\,=2^\\var{m+n}. \\end{split}\\]

Use this link to find some resources which will help you revise this topic.

Simplifying expressions from $5^m\\div 5^n$ to $5^{m-n}$.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following as a single power of 5.

\\[5^\\var{m}\\div 5^\\var{n}\\]

", "advice": "

To simplify $5^\\var{m}\\div 5^\\var{n}$, we want to make use of the following rule:

\\[a^n \\div a^m = a^{n-m}\\]

Applying this rule,

\\[\\begin{split}5^\\var{m}\\div 5^\\var{n} &\\,=5^{\\simplify[!collectNumbers]{{m}-{n}}}\\\\ \\\\&\\,=5^\\var{m-n}. \\end{split}\\]

Use this link to find some resources which will help you revise this topic.

Simplifying expressions from $3^m\\div 3^n$ to $5^{m-n}$ where $n$ can be bigger then $m$.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following as a single power of 3.

\\[\\frac{3^\\var{m}}{3^\\var{n}}\\]

", "advice": "

To simplify $\\frac{3^\\var{m}}{3^\\var{n}}$, we want to make use of the following rule:

\\[a^n \\div a^m = a^{n-m}\\]

Applying this rule,

\\[\\begin{split}\\frac{3^\\var{m}}{3^\\var{n}} &\\,=3^{\\simplify[!collectNumbers]{{m}-{n}}}\\\\ \\\\&\\,=3^{\\var{m-n}}. \\end{split}\\]

Use this link to find some resources which will help you revise this topic.

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Simplifying expressions from $(8^m)^n$ to $8^{mn}$.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following as a single power of 8.

\\[\\left(8^\\var{m}\\right)^\\var{n}\\]

", "advice": "

To simplify $\\left(8^\\var{m}\\right)^\\var{n}$, we want to make use of the following rule:

\\[\\left(a^\\var{m}\\right)^\\var{n} = a^{m\\times n}\\]

Applying this rule,

\\[\\begin{split}\\left(8^\\var{m}\\right)^\\var{n} &\\,=8^{\\var{m}\\times\\var{n}}\\\\ \\\\&\\,=8^\\var{m*n}. \\end{split}\\]

Use this link to find some resources which will help you revise this topic.

Simplifying expressions from $x^mx^n$ to $x^{m+n}$.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following as a single power of $x$.

\\[x^\\var{m}\\times x^\\var{n}\\]

", "advice": "

To simplify $x^\\var{m}\\times x^\\var{n}$, we want to make use of the following rule:

\\[a^n \\times a^m = a^{n+m}\\]

Applying this rule,

\\[\\begin{split}x^\\var{m}\\times x^\\var{n} &\\,=x^{\\simplify[!collectNumbers]{{m}+{n}}}\\\\ \\\\&\\,=x^\\var{m+n}. \\end{split}\\]

Use this link to find some resources which will help you revise this topic.

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Simplifying expressions from $y^m\\div y^n$ to $y^{m-n}$.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following as a single power of y.

\\[y^\\var{m}\\div y^\\var{n}\\]

", "advice": "

To simplify $y^\\var{m}\\div y^\\var{n}$, we want to make use of the following rule:

\\[a^n \\div a^m = a^{n-m}\\]

Applying this rule,

\\[\\begin{split}y^\\var{m}\\div y^\\var{n} &\\,=y^{\\simplify[!collectNumbers]{{m}-{n}}}\\\\ \\\\&\\,=y^{\\var{m-n}}. \\end{split}\\]

Use this link to find some resources which will help you revise this topic.

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Simplifying expressions from $(z^m)^n$ to $z^{mn}$.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following as a single power of z.

\\[\\left(z^\\var{m}\\right)^\\var{n}\\]

", "advice": "

To simplify $\\left(z^\\var{m}\\right)^\\var{n}$, we want to make use of the following rule:

\\[\\left(a^\\var{m}\\right)^\\var{n} = a^{m\\times n}\\]

Applying this rule,

\\[\\begin{split}\\left(z^\\var{m}\\right)^\\var{n} &\\,=z^{\\var{m}\\times\\var{n}}\\\\ \\\\&\\,=z^\\var{m*n}. \\end{split}\\]

Use this link to find some resources which will help you revise this topic.

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