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Simplify each of the following expressions, giving your answer in its simplest form.

Click 'Show steps' for guidance on which index law is applicable.

To enter an indice use the '^' symbol, i.e. $x^2$ will be entered as x^2

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Simplifying indices.

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Recall the laws of indices to help solve the problems:

$x^a \\times x^b = x^{a+b}$

$x^a \\div x^b = x^{a-b}$

$x^{-a} = \\frac{1}{x^a}$

$(x^a)^b = x^{ab}$

$(\\frac{x}{y})^a = \\frac{x^a}{y^a}$

$x^\\frac{a}{b} = (\\sqrt[b]{x})^{a}$

$x^0 = 1$

Worked Solutions:

Part a) $p^{(\\var{c}+\\var{d})}=\\simplify{p^{({c}+{d})}}$

Part b) $c^{(\\var{a}-\\var{b})}=c^\\simplify{({a}-{b})}$

Part c) $\\frac{6^\\var{g}}{9^\\var{h}}\\times{p^{\\var{h}\\var{j}-\\var{g}\\var{f}}}=\\simplify{(6^{g})/(9^{h})*p^{h*j-g*f}}$

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$p^\\var{c} \\times p^\\var{d}$

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Use the following law to help answer this question:

$x^a \\times x^b = x^{a+b}$

$c^\\var{a}$$c^\\var{b}$

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Use the following law:

$x^a \\div x^b = x^{a-b}$

$(6p^{-\\var{f}})^{\\var{g}}$$(9p^{-\\var{j}})^{\\var{h}}$

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Using principles of BODMAS, the brackets need to be expanded first.

Now you are left with a dividend and divisor,

which can be simplfied according to the known patterns of indices.

i.e.

$\\frac{ax^c}{bx^d}= \\frac{a}{b}x^{(c-d)}$

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